Question

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).
253, comma, 248, comma, 243, comma, dot dot dot
253,248,243,...
Find the 49th term.
Find the 49th term.

Answer 1

To find the 49th term of the sequence given by the first three terms: 253, 248, 243, we first observe the pattern in the sequence.

The difference between the first two terms (253 and 248) is:

\[ 248 - 253 = -5 \]

The difference between the second and third terms (248 and 243) is:

\[ 243 - 248 = -5 \]

This shows that the sequence decreases by 5 each time, indicating that it's an arithmetic sequence with a common difference \(d = -5\).

The formula for the \(n\)-th term of an arithmetic sequence can be expressed as:

\[
a_n = a_1 + (n-1) \cdot d
\]

where:
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

In this case:
- \(a_1 = 253\)
- \(d = -5\)

To find the 49th term (\(n = 49\)):

\[
a_{49} = 253 + (49 - 1) \cdot (-5)
\]

Calculating this step by step:

1. Calculate \(n - 1\):
\[
49 - 1 = 48
\]

2. Multiply by the common difference:
\[
48 \cdot (-5) = -240
\]

3. Add to the first term:
\[
a_{49} = 253 + (-240) = 253 - 240 = 13
\]

Thus, the 49th term of the sequence is:

\[
\boxed{13}
\]